2 Chapter Objectives Be able to: Describe the various roles of inventory, including the different types of inventory and inventory drivers.Distinguish between independent demand and dependent demand inventory.Calculate the restocking level for a periodic review system.Calculate the economic order quantity (EOQ) and reorder point (ROP) for a continuous review system.Determine the best order quantity when volume discounts are available.Calculate the target service level and target stocking point for a single-period inventory system.Describe how inventory decisions affect other areas of the supply chain. In particular, be able to describe the bullwhip effect, inventory positioning issues, and the impact of transportation, packaging, and material handling considerations.
3 Inventory Management Functions, forms, and drivers of inventory Inventory cost issuesTools: Economic order quantity (EOQ) Reorder point (ROP) and safety stock Dealing with quantity discounts
5 Four Inventory Drivers Demand and Supply UncertaintiesSafety stock, hedge inventoryDemand and Process Volume MismatchesCycle stockDemand and Capacity MismatchesSmoothing inventoryDemand and Supply Lead-Time MismatchesAnticipation inventory, transportation inventory
6 Independent Demand Demand from outside the organization Unpredictable usually forecastedDemand for tables . . .
7 Dependent Demand Tied to the production of another item Relevant mostly to manufacturersOnce we decide how many tables we want tomake, how many legs do we need?
8 Two “Classic” Systems for Independent Demand Items Periodic review systemsContinuous (perpetual) review systemsFactorsOrder quantity (Q)Restocking level (R)Inventory level when reviewed (I)
9 Restocking Levels Periodic Review Continuous Review Periodic Review Here RP+L represents the reorder period plus the order lead time, mu is the average demand during that time and sigma is the standard deviation of the demand during that time.Z or zeta is the number of standard deviations chosen to achieve a desired service level.Continuous Review:Here d is the demand rate and L is the lead time for an order to come in. Obviously, variations in the demand and lead time are not accounted for since continuous review allows adjustment for some variation in these values.
10 Periodic Review System (Orders at regular intervals) Inventorylevel246Time
11 Continuous Review System (Orders when inventory drops to R) How is the reorderpoint ROP established?QInventorylevelRTimeL-Tlead time to get a new order in
12 Comparison of Periodic and Continuous Review Systems Periodic ReviewFixed order intervalsVariable order sizesConvenient to administerOrders may be combinedInventory position only required at reviewContinuous ReviewVarying order intervalsFixed order sizes (Q)Allows individual review frequenciesPossible quantity discountsLower, less-expensive safety stocks
13 Order Quantity Q and Average Inventory Level As the order quantity doublesso does the average inventory (= Q/2)Q2Q2 2Q1Q1 2
14 What is the “Best” Order Size Q? Determined by:Inventory related costsOrder preparation costs and setup costsInventory carrying costsShortage and customer service costsOther considerationsOut of pocket or opportunity cost?Fixed, variable, or some mix of the two?
15 Economic Order Quantity (EOQ) Model Cost Minimizing “Q”Assumptions:Uniform and known demand rateFixed item costFixed ordering costConstant lead time
16 What are the Total Relevant Annual Inventory Costs? Consider:D = Total demand for the yearS = Cost to place a single orderH = Cost to hold one unit in inventory for a yearQ = Order quantityThen:Total Cost = Annual Holding Cost + Annual Ordering Cost= [(Q/2) × H] + [(D/Q) × S]Comment: Can explain to students that item cost is considered when evaluating volume discountsHow do these costs vary as Q varies?Why isn’t item cost for the year included?
18 Ordering costs per year decrease as Q increases $Ordering costs per yeardecrease as Q increases(why?)(Q/2)×H(D/Q)×SQ
19 Total Annual Costs and EOQ EOQ at minimum total cost
20 EOQ SolutionWhen the order quantity = EOQ, the holding and setup costs are equal
21 Sample ProblemsPam runs a mail-order business for gym equipment. Annual demand for the TricoFlexers is 16,000. The annual holding cost per unit is $2.50 and the cost to place an order is $50. What is the economic order quantity?Using the same holding and ordering costs as above, suppose demand for TricoFlexers doubles to 32,000. Does the EOQ also double? Explain what happens.Answers: EOQ = 800; 1,131 (goes up by the square root of 2)
22 EOQ tells us how much to order... …but when should we order?Reorder point and safety stock analysis
23 Safety StockWhen both lead time and demand are constant, you know exactly when your reorder point is ...QRL
24 Safety Stock II Under these assumptions: Reorder point = total demand during the lead time between placement of the order and its receipt.ROP = d × L, whered = demand per unit time, andL = lead time in the same time units
25 Safety Stock III (Uncertainties) But what happens when either demand or lead time varies?QRL1L2
26 Safety Stock IV What causes this variance? Average demand during lead time
27 Uncertainty Drivers The variability of demand The variability of lead timeThe average length of lead timeThe desired service level2) and 3) are determined by a company’s choice of supply chain partners
28 Safety StockAdditional inventory beyond amount needed to meet “average” demand during lead timeProtects against uncertainties in demand or lead timeBalances the costs of stockouts against the cost of holding extra inventory
29 Shown Graphically …Now, what is thechance of a stockout?7%93%
30 Recalculating the Reorder Point to include Safety Stock
31 Determining “z”z = number of standard deviations above the average demand during lead timeThe higher z is:The lower the risk of stocking outThe higher the average inventory levelWhat is the average inventory level when we include safety stock?Average inventory plus safety stock level
32 Determining “z”Typical choices for z: z = 90% service level z = 95% service level z = 99% service levelWhat do we mean by “service level”?
33 Reorder Point + Safety Stock Formula: What happens if lead time is constant?What happens if the demand rate is constant?What happens if both are constant?If you wanted to reduce the amount of safety stock you hold, what is your best option?
34 Problems I One of the products stocked by Sam’s Club is SamsCola. During the slow season, the demand rate is approximately 650 cases a month, which is the same as a yearly demand rate of 650×12 = 7,800 cases.During the busy season, the demand rate is approximately 1,300 cases a month, or 15,600 cases a year.The cost to place an order is $5, and the yearly holding cost for a case of SamsCola is $12.
35 Problems II According to the EOQ formula: How many cases of SamsCola should be ordered at a time during the slow season?How many cases of SamsCola should be ordered during the busy season?Slow season: 81 casesBusy season: 114 cases
36 Problems IIIDuring the busy season, the store manager has decided that 98 percent of the time, he does not want to run out of SamsCola before the next order arrives. Use the following data to calculate the reorder point for SamsCola.Weekly demand during the busy season: 325 cases per weekLead-time: 0.5 weeksStandard deviation of weekly demand: 5.25Standard deviation of lead-time: 0 (lead-time is constant)Number of standard deviations above the mean needed to provide a 98% service level (z): 2.05Answer: 170 cases
37 Quantity Discounts I What effect will quantity discounts have on EOQ? D = 1,200 units (100×12 months)H = $10 per unit per yearS = $30.00 ordering costOrder Size Price$35.0090 and up $32.50Note: When H is a cost based on a percent of the value of the item, these calculations become more complicated, but are done in the same way.
38 Quantity Discounts II 1. Calculate the EOQ for the non discount price: 2. If we can order this quantity AND get the lowest price, we’re done. Otherwise ...
39 Quantity Discounts III Compare total holding, carrying, AND item cost for the year at: Each price break The first feasible EOQ quantityDo you understand why we must now look at item cost for the year?
40 Quantity Discounts IV Total costs at an order quantity of 85: (85/2)×$10 + (1200/85)×$ ×$35.00 =$ $ $42,000 = ??Total costs at an order quantity of 90:(90/2)×$10 + (1200/90)×$ ×$32.50 =$ $ $39,000 = ??Quantity 85: $42,848.53Quantity 90: $39,850
41 Conclusions:When all costs are considered, it is cheaper to order 90 at a time and take the price discount.When there are volume discounts, the EOQ calculation might be infeasible or might not result in lowest total cost.If holding cost is a percentage of the item value (a common practice for more expensive items), analysis is more complex, but done the same way
42 Single-Period Inventory (When safety stock is not an option) Inventory is perishableNewspapers, periodicalsFresh food, Christmas treesMust balance costs ofBeing short = profit lostHaving excess = item cost + disposal cost – salvage valueRequires a target service level that best balances shortage and excess costs
43 Target Service LevelSets expected shortage cost = expected excess costOr (1–p) × Cshortage = p × CexcessWhere p = probability of enough units to meet demand, (1–p) = probability of shortageHence solving for p where the top equation is true provides the target service levelSLT = Cshortage / (Cshortage + Cexcess)
44 Target Stocking Point Must know how demand is distributed Is it roughly the same every day?Are there different demand distributions?In all cases, develop the cumulative probability distribution for the demand levels in order of increasing demand and select demand level whose corresponding cumulative probability is nearest to the target service level.
46 Inventory in the Supply Chain Bullwhip EffectSmall demand changes large order variationsInventory PositioningCost and value increases, flexibility decreases down the supply chain where do we hold inventory?Transportation, Packaging, Material HandlingPhysical size and quantity of lot, how it is packaged, handling equipment needed,and disposal of packaging are all factors in choosing appropriate supplier and distribution process
48 Case Study in Inventory Management Northcutt Bikes: The Service Department
49 Supplement ABC Classification Method IDEACompanies have thousands of items to trackMethods like EOQ only justifiable for most important items.
50 ABC Method Determine annual $ usage for each item Rank the items according to their annual $ usageLet:Top 20% “A” items roughly 80% of total $Middle 30% “B” items roughly 15% of total $Bottom “50% “C” item roughly 5% of total $
51 ABC Analysis Example Total $ Usage = $98,500 Item Cost Demand $ Usage $46200$9,200B2$4010$400C3$56680$33,400D4$81100$8,100E5$2250$1,100F6$6$600G7$176250$44,000H8150$900I9$10$100J10$14$700Total $ Usage = $98,500
52 Ranking by Annual $ Usage Item$ UsageCumulative $ Usage% of Total $ UsageClassG7$44,00044.67%AC3$33,400$77,40078.58%A1$9,200$86,60087.92%BD4$8,100$94,70096.14%E5$1,100$95,80097.26%H8$900$96,70098.17%CJ10$700$97,40098.88%F6$600$98,00099.49%B2$400$98,40099.90%I9$100$98,500100.00%